Rewrite as a simplified fraction. ${1.12\overline{4} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1124.4444...\\ 100x &= 112.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1012}$ ${x = \dfrac{1012}{900}} $ ${x = \dfrac{253}{225}} \text{or} {1 \dfrac{28}{225}}$